What does the '76' in Soldier 76's name represent?

Solution 1:

The most accurate guess to this is because:

Before long, he earned a coveted position in the government's controversial and still-classified (but widely acknowledged) "soldier enhancement program." Source

He is assumed to be the 76th Soldier to be accepted into this program.

His origin story is highly classified and there is no definitive proof as to what 76 means, but this is the closest answer in my opinion.

Solution 2:

If you go into a custom game with multiple Soldier 76s, their number values will increase. It may be a hint from blizzard that he is a clone. (Or just an easter egg)

Solution 3:

His name's obviously a reference to USA's founding year 1776. The character had been conceptualized and named by Metzen long before Overwatch existed.